Optimal Determination of Space Objects Orbit by Angular Measurements of Ground-Based Optoelectronic Stations

The successful solution of practical cosmonautics problems is largely achieved by contemporary advances in measurement and computing technology, as well as by improvements in methods of primary and secondary processing of trajectory measurements. Therefore, in long-range programs of space exploration and space technology development, much attention is paid to improving existing and developing new algorithmic and technical means of navigation support for flights of space objects with the purpose to expand capabilities and increasing the efficiency of autonomous navigation systems of spacecraft, as well as ground-based and perspective orbital systems of space monitoring. Currently, active work is underway to modernize and develop promising complexes of specialized optoelectronic devices for monitoring near-Earth space based on angular measurements. The article considers the application of the variational approach for solving problems of statistical estimation of the trajectory parameters of the orbital object by angular measurements, which were carried out by ground-based optoelectronic means that are part of the modern space control system. Models and algorithms for determining estimates of orbital parameters that implement the variational version of the maximum likelihood method are presented, as well as the results of test calculations related to iterative solution of the two-point boundary value problem of variational estimation. The main purpose of the numerical calculations  is a study of convergence of the proposed estimation algorithm, as well as the impact of measurement errors on the displacement of the obtained estimates relative to their exact values. The simulation results, presented in the article, correspond to the conditions of the orbital motion of METEOR PRIRODA spacecraft and were obtained using the ephemeris data of the NORAD catalog in TLE-elements.